Equations of Lines (rearranging the furniture). There are three different forms of the equation of a...
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Transcript of Equations of Lines (rearranging the furniture). There are three different forms of the equation of a...
Equations of Lines(rearranging the furniture)
There are three different forms of the equation of a line.
Two are for “show”:
slope-intercept equation of a line: y = mx + b
standard equation of a line: Ax + By = C
And one is a “workhorse”:
point-slope equation of a line: y – y1 = m( x – x1)
Three Forms of Linear Equations
The point-slope equation of a line: y – y1 = m( x – x1)
is used to figure out the equation of a line
when you are given a point and the slope.
You never give your answer in point-slope form.
Point-slope Equation of a Line
The slope-intercept equation of a line: y = mx + b
is great for graphing.
m is the slope of the line
(0, b) is the y-intercept of the line
You frequently are asked to give your answer in point-slope form.
Slope-intercept Equation of a Line
The standard equation of a line: Ax + By = C
is mainly for show.
You frequently are asked to give your answer in standard form.
Standard Equation of a Line
If they tell you that the slope is
And the y-intercept is (0, – 5)
The slope intercept equation is y = x – 5
Slope-intercept Form
7
4
7
4
The slope intercept equation is y = x – 5
To write that in standard form, first multiply each term by the LCD.
4y = 7x – 20
Then rearrange the furniture.
– 7x + 4y = – 20
7x – 4y = 20
From slope-intercept to Standard Form
7
4
Make x positive
What if they ask you to graph
7x – 4y = 20
Then rearrange the furniture – solve for y
– 4y = 7x – 20
y = x – 5
Now you know the slope and the y-intercept and it’s easy to graph!
From Standard to slope-intercept Form
7
4
Equations of lines
Point-slope: never the form of an answer.
Slope-intercept: Great for graphing. May be requested for an answer.
Standard form: Frequently requested for answers.